How Richard Dawkins might explain a tennis coincidence

[Did this for my Sunday Guardian books column]

“Look into a mirror for a lifetime,” said the poet-filmmaker Jean Cocteau, “and you see Death doing its work.” Having watched nearly half of the eleven-hour match that John Isner and Nicolas Mahut contrived to play at Wimbledon last year, I’d say no mirror is necessary.

If you follow tennis, even casually, you may have heard about the gasps of astonishment at the Wimbledon draw ceremony last week when Isner and Mahut were again drawn to play each other in the first round. This has opened the conspiracy-theory floodgates. Their 2010 match, soul-annihilating though it was, probably got more media coverage and public attention (especially outside sporting circles) than any Slam final. “Arranging” a sequel could be good for ticket sales – so was the draw rigged?

Personally I doubt it: the draw process is a transparent one and the ceremony very public. But the rhetorical question “What are the chances of such a thing happening just randomly?” continues to be asked by tennis fans everywhere – the implication being that this couldn’t have been a coincidence; that organisational (or occult) forces had to be at work.

Actually, the odds aren’t close to astronomical. I won’t bore you with the calculations, but keeping in mind that Isner and Mahut were both among 96 unseeded players, the chance that they would play each other works out to something like 1 in 140, or 0.7 percent. Improbable, yes, but hardly mind-boggling as these things go. Even if you calculate the chance of their meeting in the first round in successive years, you don’t get wildly unlikely numbers. (In fact, the coincidence of the same two players meeting in the 1st round in consecutive Wimbledons has occurred eight times since 1970.)

My favourite writings on the phenomenon of coincidences and how the human mind can get excessively excited about them are in Richard Dawkins’ Unweaving the Rainbow, specifically in the chapters "Hoodwink'd with Faery Fancy" and "Unweaving the Uncanny". Dawkins begins with a simple enough incident: a four-digit personal code number issued to him by his college was exactly the same as the safety code he had just chosen for his bicycle lock. The probability of this happening is 1 in 10,000 – seemingly very large odds – but as he points out, “the number of people in the world is so large compared with 10,000 that somebody, at this very moment, is bound to be experiencing a coincidence at least as startling as mine. It just happens that today was my day to notice such a coincidence.”

Each ordinary day that you or I live through is an unbroken sequence or events, or incidents, any of which is potentially a coincidence. I am now looking at a picture on my wall of a deep-sea fish with a fascinatingly alien face. It is possible that at this very moment, the telephone will ring and the caller will identify himself as a Mr Fish. I'm waiting...

On another occasion his wife bought an antique watch as a gift for her mother, then discovered that the watch had her mother’s initials – “M.A.B.” – engraved on the back. Many people I know, if faced with this situation, would hasten to invoke supernatural causes (presumably because the invisible pink unicorn in the sky has nothing better to do with Her time than spring pleasant little surprises on randomly selected homosapiens), but Dawkins takes out the phone book, checks the frequency of names beginning with M, A and B and then sets about his calculations. It turns out that if each of the 55 million people in Britain bought an engraved watch, we could expect nearly 20,000 of them to experience a coincidence of this magnitude.

Much heft is added to Dawkins' argument by the concept of the PETWHAC (Population of Events That Would Have Appeared Coincidental), a term he coins to show how the pattern-seeking mind can make coincidences appear even more remarkable than they are. (If his wife had discovered the initials of her mother’s maiden name on the watch, or her own initials for that matter, it would have seemed just as impressive – but it would also mean a broadening of the PETWHAC, which would further increase the probability of a coincidence.) Public “mystics” and “psychics” dine out on this sort of gullibility and pattern-seeking all the time.

(More about the PETWHAC here)

Incidentally the title Unweaving the Rainbow comes from John Keats’ observation that science had destroyed the beauty of the rainbow by “explaining” its colours. Dawkins’ response is that the natural world as revealed by scientific understanding can be beautiful and awe-inspiring. “Disarming apparently uncanny coincidences is more interesting than gasping over them,” he says. Whether or not you agree with him, I’d say analysing mathematical probabilities is much more interesting than watching another Isner-Mahut match. Even if you hate maths.

[Here's an old post on Dawkins' Climbing Mount Improbable. And a little more about Unweaving the Rainbow in the postscript of this post.]

Update: Just realised that the Serious Men post I linked to above was written on this day exactly a year ago - now there's another good coincidence for you! (And I swear it wasn't planned.)